Group Title: investigation of the strength of concrete masonry shear wall structures
Title: An investigation of the strength of concrete masonry shear wall structures
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Title: An investigation of the strength of concrete masonry shear wall structures
Physical Description: xxii, 228 leaves. : illus. ; 28 cm.
Language: English
Creator: Balachandran, Krishnaiyer, 1942-
Publication Date: 1974
Copyright Date: 1974
 Subjects
Subject: Concrete walls   ( lcsh )
Strength of materials   ( lcsh )
Shear (Mechanics)   ( lcsh )
Masonry   ( lcsh )
Civil Engineering thesis Ph. D
Dissertations, Academic -- Civil Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis -- University of Florida.
Bibliography: Bibliography: leaves 221-226.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00098326
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000582505
oclc - 14116875
notis - ADB0880

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AN INVESTIGATION OF THE STRENGTH
OF CONCRETE MASONRY SHEAR WALL STRUCTURES










By

KRISHNAIYER BALACHANDRAN


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY








UNIVERSITY OF FLORIDA


1974














ACKNOWLEDGMENTS


The author wishes to express his sincere gratitude to

Dr. M. W. Self for his patience, guidance, and encouragement,

without which this dissertation would not have been possible.

Special thanks are due to Prof. Herbert A. Sawyer, Jr.,

for sparing some of his equipment and literature and, also,

for serving on the supervisory committee. Appreciation is

extended to Dr. C. S. Hartley for serving on his supervisory

committee.

Sincere thanks are due to Dr. Martin A. Eisenberg for

the help he has provided in introducing the author to the

Finite Element Method. Without his professional guidance,

helpful suggestions and long hours of discussion, the

author's task would have been more difficult.

The author wishes to express his gratitude to all

those who assisted him along the way: Graduate students

K. Fuller and M. Chanchalani; and friends M. Krishnamurthy,

S. M. Ulagaraj, J. N. Sharma, A. M. Garde and H. A. Cole, Jr.

Thanks are due to Mr. L. F. Hopkins and W. Whitehead

for their help on the equipment in the Civil Engineering

Laboratory.


iii










Acknowledgment is due to the Concrete Promotion

Council of Florida for their financial support for part of

the experimental program; to the National Concrete Masonry

Association and the National Bureau of Standards for provid-

ing the model concrete blocks; and, to the Northeast

Regional Data Center for its support.

Special thanks go to Mrs. C. Combs for her concerned

work when typing the final copy.

Finally, a special note of deep appreciation is due

to his wife, Lalitha, for her encouragement, love and

understanding during the difficult time of being the wife

of a student.















TABLE OF CONTENTS


Page
ACKNOWLEDGMENTS ......................................... iii

LIST OF TABLES........................................ viii

LIST OF FIGURES....................................... ix

KEY TO SYMBOLS........................................ xv

ABSTRACT.............................................. xxi

CHAPTER

1. INTRODUCTION................................... 1

1.1 History .................................... 1
1.2 General Remarks............................ 2
1.3 Previous Investigations................... 6
1.3.1 Strength of Mortar Joints......... 6
1.3.2 Racking Tests...................... 10
1.3.3 Circular Shear Specimens.......... 12
1.3.4 Square Shear Specimens............ 13
1.3.5 Horizontally and Vertically
Loaded Wall Without Frame........ 16
1.3.6 Test on Small Masonry Assemblages. 17
1.3.7 Reinforced Concrete Masonry
Walls in Shear.................. 20
1.3.8 Effect of Wall Openings........... 22
1.3.9 Shear in Concrete Masonry Piers... 25
1.3.10 Strength of Masonry under
Combined Compression and Shear.. 30
1.4 Objectives and Scope of Present
Investigation............................. 33

2. EQUIPMENT, MATERIALS AND TESTING TECHNIQUES.... 35

2.1 Testing Machines and Other Equipment....... 35
2.2 Concrete Blocks ............................ 36
2.3 Mortar ..................................... 39
2.4 Model Concrete Blocks ..................... 41
2.5 Model Reinforcement....................... 43
2.6 Model Mortar ............................... 43
2.7 Model Grout Mixes.......................... 46
2.8 Mortar Mix for Spandrel................... 51











Table of Contents (Continued)


CHAPTER Page
3. STRENGTH OF MORTAR JOINTS UNDER
COMBINED STRESSES.. ........................... 52

3.1 Scope ...................................... 52
3.2 Test Specimens ............................ 53
3.3 Strength of Mortar Joints under
Compression and Shear.................... 53
3.4 Strength of Mortar Joints under
Compression and Bending................. 63
3.5 Combined Compression, Bending, and Shear.. 69

4. MODEL TESTS OF CONCRETE MASONRY PIERS........... 70

4.1 Selection of Model........................ 70
4.2 Selection of Model Materials............... 83
4.3 Fabrication of Model....................... 86
4.4 Test Setup................................. 89
4.5 Test Parameters............................. 91
4.6 Tests on Grouted Piers..................... 91
4.7 Tests on Nongrouted Piers.................. 101

5. ANALYSIS OF TEST RESULTS....................... 102

5.1 Grouted Piers............................. 102
5.2 Nongrouted Piers ........................ .. 105
5.3 Equations for Predicting the Diagonal
Tensile Strength of Masonry.............. 108
5.3.1 Grouted Piers...................... 108
5.3.2 Nongrouted Piers.................... 111

6. NONLINEAR FINITE ELEMENT ANALYSIS.............. 122

6.1 General Remarks........................... 122
6.2 Finite Element Linear Analysis............ 123
6.3 Finite Element Nonlinear Analysis.......... 125
6.3.1 General Remarks.................... 125
6.3.2 General Physical Approach.......... 126
6.4 Variable Stiffness Methods................ 127
6.5 Initial Stress Method...................... 130
6.6 Initial Strain Method..................... 131
6.7 Previous Investigations.................... 132
6.8 Objective and Scope of Present
Investigation............................ 138

7. DESCRIPTION OF ANALYTICAL MODEL................ 139

7.1 Choice of Finite Elements................. 139
7.2 Formulation of Element Stiffness Matrix... 142











Table of Contents (Continued)


CHAPTER Page
7. Description of Analytical Model (Continued)....

7.3 Material Properties and Failure Criteria.. 147
7.3.1 Uniaxial Stress-Strain Curves....... 147
7.3.2 Representation of Properties
of Masonry Element............... 147
7.3.3 Plastic Yielding in Compression.... 152
7.3.4 Biaxial Strength of a
Masonry Component................ 153
7.3.5 Crushing of Masonry................ 155
7.3.6 Cracking............................ 155
7.3.7 Bond Failure at the Interface
between Mortar and Block.......... 159
7.3.8 Yielding of Reinforcement.......... 164

8. ANALYSIS AND EXAMPLES.......................... 165

8.1 Method of Solution..... .................... 165
8.2 Computational Procedure................... 167
8.3 Computer Program........................... 172
8.4 Examples of Nonlinear Analysis............ 175
8.4.1 Square Concrete Panel under
Diagonal Compression.............. 175
8.4.2 Hollow Concrete Masonry Panels
under Diagonal Compression....... 182
8.4.3 Grouted Masonry Piers............... 188
8.4.4 Nongrouted Masonry Piers............ 198

9. CONCLUSIONS.................................... 203

9.1 Conclusions. .............................. 203
9.2 Recommendations for Further Study.......... 207

APPENDIX A (ALGORITHM FOR SOLUTION OF EQUATIONS) ...... 208

APPENDIX B (COMPUTER PROGRAM OUTPUT) .................. 213

REFERENCES..... ........ ............................... 221

BIOGRAPHICAL SKETCH................................... 227


vii















LIST OF TABLES


TABLE Page
2.1 PROPERTIES OF MODEL MORTAR AND GROUT............ 48

3.1 PROPERTIES OF MORTAR....... ............... ...... 54

3.2 STRENGTH OF MORTAR JOINTS UNDER
COMPRESSION AND SHEAR......................... 58

3.3 STRENGTH OF 1:1:4.5 MORTAR JOINTS UNDER
COMPRESSION AND SHEAR......................... 59

3.4 STRENGTH OF MORTAR JOINTS UNDER
COMPRESSION AND BENDING....................... 62

3.5 MORTAR JOINTS UNDER COMBINED
COMPRESSION, BENDING, AND SHEAR............... 67

5.1 TEST RESULTS OF GROUTED PIERS................... 103

5.2 TEST RESULTS OF NONGROUTED PIERS................ 109

5.3 ANALYSIS OF RESULTS OF TESTS ON NONGROUTED
PIERS......................................... 115

8.1 MATERIAL PROPERTIES USED IN ANALYSIS OF PR 3.... 190

8.2 MATERIAL PROPERTIES USED IN ANALYSIS OF PR 7.... 195

8.3 MATERIAL PROPERTIES USED IN ANALYSIS OF PR 9.... 197


viii















LIST OF FIGURES


FIGURE Page
1.1 Shear wall with boundary elements............... 5

1.2 Elements of shear wall with openings............ 5

1.3 Type of test specimens used by Zelger.......... 8

1.4 Test specimen adopted by Haller................ 8

1.5 Arrangement of racking test and the force
distribution on the specimen................. 11

1.6 Test for diagonal tensile strength of
brickwork and stress distribution............. 11

1.7 Typical X-cracks in a wall damaged by
an earthquake................................ 14

1.8 Fringe patterns obtained in a photoelastic
analysis of a model of a wall with an
opening and a square panel under
diagonal compression......................... 14

1.9 Diagonal tension test on a square panel......... 15

1.10 Test setup (schematic) adopted by Meli and
Reyes for testing mortar joints under
compression and shear........................ 15

1.11 Types of test specimens adopted by Meli and
Reyes for diagonal compression tests......... 19

1.12 Test panels adopted by Converse................ 19

1.13 Continuous opening in a shear wall............. 23

1.14 Staggered opening in a shear wall............... 23

1.15 Forces acting on a pier element
in a wall with opening....................... 26

1.16 Test setup adopted by Schneider for full scale
test on piers................................ 26










List of Figures (Continued)


FIGURE Page
2.1 Splitting tests on concrete block............... 38

2.2 Sieve analysis of sand for masonry mortar...... 40

2.3 Model concrete block........................... 42

2.4 Model reinforcement (0.147" dia.).............. 42

2.5 Stress-strain curve for model concrete block... 44

2.6 Stress-strain curve for model reinforcement.... 45

2.7 Stress-strain curve for model mortar............ 47

2.8 Stress-strain curve for model grout............. 49

2.9 Stress-strain curve for spandrel mortar......... 50

3.1 Setup for studying the strength of mortar
under pure shear............................. 55

3.2 Test setup for finding the strength of mortar
joints under combined compression and shear.. 56

3.3 Shear failure through mortar joint............. 56

3.4 Effect of precompression on the shearing
strength of mortar joints.................... 60

3.5 Cross-section of a mortar joint................. 64

3.6 Effect of precompression on the flexural
tensile strength of mortar joints............ 65

3.7 Test setups used for obtaining combined
stresses on mortar joints.................... 66

3.8 Interaction of bending and shear
under constant precompression................ 68

4.1 Photoelastic model configurations
chosen by Schneider.......................... 71

4.2 Finite element idealization for a shear wall
with openings.................................. 73











List of Figures (Continued)

FIGURE


Page


4.3 Finite element idealization for a
multiple pier shear wall.....................

4.4 Finite element idealization for a
pier with openings and walls on either side..

4.5 Finite element idealization for the test
specimen adopted by Schneider.................

4.6 Isoshear lines for the pier shaded as shown
above ........................................

4.7 Isoshear lines for the pier shaded as shown
above ........................................

4.8 Isoshear lines for the pier shaded as shown
above ........................................

4.9 Isoshear lines for the pier shaded as shown
above ........................................

4.10 Isoshear lines for the pier shaded as shown
above ........................................

4.11 Isoshear lines for the pier shaded as shown
above.........................................

4.12 Schematic test setup for finding the
shearing strength of a pier..................

4.13 Details of pier model..........................

4.14 Model test on pier .............................

4.15 Failure pattern of PR 4 strong mortar,
weak grout ...................................

4.16 Failure pattern of PR 3 strong mortar,
medium grout .................................

4.17 Failure pattern of PR 5 strong mortar,
strong grout..................................

4.18 Failure pattern of PR 9 weak mortar,
weak grout....................................

4.19 Failure pattern of PR 10 weak mortar,
medium grout..................................











List of Figures (Continued)

FIGURE


xii


Page


4.20 Failure pattern of PR 7 weak mortar,
strong grout.................................

4.21 Typical load-deflection curves for
grouted piers ............................ ....

4.22 Failure pattern of PR 13 weak mortar,
precompression 50 psi........................

4.23 Failure pattern of PR 23 weak mortar,
precompression 125 psi........................

4.24 Failure pattern of PR 17 weak mortar,
precompression 200 psi.......................

4.25 Failure pattern of PR 19 strong mortar,
precompression 50 psi........................

4.26 Failure pattern of PR 21 strong mortar,
precompression 125 psi.......................

4.27 Failure pattern of PR 20 strong mortar,
precompression 200 psi.......................

4.28 Failure pattern of hollow pier PR 1
(strong mortar) ........................... ..

4.29 Failure pattern of hollow pier PR 6
(weak mortar).............................. ...

5.1 Relation between average shear stress and
square root of prism strength for grouted
piers.........................................

5.2 Comparison of results of grouted piers
with corresponding prism strengths............

5.3 Area used to compute shear stress for
hollow piers .............................. ...

5.4 Effect of precompression on shearing strength
of nongrouted piers..........................

5.5 Idealization for a pier loaded in
diagonal compression..........................

5.6 Test results of nongrouted pier specimens......

5.7 Failure pattern of hollow square panel
subject to diagonal compression..............


94


95


96


96


97


97


98


98


99


100



104


106


107


110


112

113


118










List of Figures (Continued)

FIGURE
5.8 Assumed state of stress at the
center of pier................................

6.1 Effect of nonlinear material properties........

6.2 Iterative solution techniques for
nonlinear analysis............................

6.3 Material idealization and selected results
of analysis of RC panels by
Cervenka and Gerstle.........................

6.4 Failure envelope adopted by Franklin............

6.5 Schematic diagram to illustrate crack
propagation (initial stress method using
variable stiffness within an increment)......

6.6 Schematic diagram to illustrate crack
propagation (initial stress method using
constant stiffness within an increment)......

7.1 Solution of a cantilever beam by elements
with varying degrees of freedom..............

7.2 Quadratic rectangular element..................

7.3 Uniaxial stress-strain curves ..................

7.4 Components of a reinforced grouted element.....

7.5 Rotation of coordinates.......................

7.6 Liu's failure envelope for concrete
under biaxial compression....................

7.7 Assumed failure envelope for block,
mortar, and grout............................

7.8 Cracking at an integration point................

7.9 Bond strength criterion.........................

7.10 Normal stresses acting on interface
of inclined mortar joints....................

8.1 Schematic diagram illustrating the
nonlinear analysis adopted...................


xiii


Page

119

128


128



133

135



137



137


141

141

148

150

150


154


154

157

157


162


166











List of Figures (Continued)

FIGURE


xiv


8.2 General flow chart of the program................

8.3 Flow diagram for the failure criteria............

8.4 Crack pattern of square concrete panel
at 195,000 lbs ................................

8.5 Crack pattern of square concrete panel
at 196,000 lbs ................................

8.6 Crack pattern of square concrete panel
at 197,000 lbs ................................

8.7 Crack pattern of square concrete panel
at 198,000 lbs ................................

8.8 Crack pattern of square concrete panel
at 199,000 lbs ................................

8.9 Experimentally observed failure modes
in hollow concrete masonry panels..............

8.10 Predicted failure pattern for panel SM...........

8.11 Predicted failure pattern for panel MS...........

8.12 Predicted failure pattern for panel MW...........

8.13 Finite element idealization for pier PR 3.......

8.14 Predicted crack pattern for PR 3................

8.15 Analytical and experimental load-deflection
curves for grouted piers......................

8.16 Predicted failure pattern for PR 7...............

8.17 Predicted failure pattern for PR 9..............

8.18 Predicted failure pattern for PR 6..............

8.19 Predicted failure pattern for PR 19.............

B.1 Finite element idealization for panel SM.........


Page
173

174


176


178


179


180


181


183

184

186

187

189

192


193

196

199

200

201

215















KEY TO SYMBOLS


A sectional area of split in the indirect tension
test on concrete block; area of cross-section
of pier.

A c-ross-sectional area of block.

Sarea of cross-section of go.out.

area of cross-section of steel reinforceIment

a distance from the point of inflection to tht-
spandrel restraint; length of a grouted f nit :
element.

a location of integration point j' in the Gci::
quadrature formula.

iBn matrix relating element strains to nolal
displacements.

{R1) matrix of stiffness coefficients which relates the
unknown displacements in (,ol(nun I with those of
column 2.

C initial bond strength between brick and mortar.

{CL, matrix of stiffness coefficients which relates the
the unknown displacements in column 1 with those
of column 3.

c .'-hesion between mortar and block.

lI diameter of specimen; overall pier depth.

il ] square matrix of stiffness coefficients whicl reelates
the unknown displacements of column 1 among
themselves.

I' global constitutive matt.ix al thi- pu.iit or
occurrence of compression-shear debonding.

[D local constitutive matrix at the point of
occurrence of compression-shear debonding.


xv











Key to Symbols (Continued)


[D cr] rigidity matrix for cracked point in the global
frame of reference.

[D cro material stiffness matrix for cracked ccr:.ie
in the local principal coordinate system.

[) i] lasto-plastic matrix.

LDtb] global constitutive matrix at the point of
occurrence of shear-tension debonding.

d width of specimen.

E Young's modulus of steel reinforcement.

EB initial tangent modulus of elasticity of block.

EG initial tangent modulus of elasticity of grout.

ES Young's modulus of steel reinforcement.

E equivalent modulus of elasticity of a composite
e element.

F applied load; plasticity factor.

{F} element nodal forces.

{F,} RHS vectors for unknowns in column 1.

f material stresses; function of stress and strain.

f external precompression on mortar joints, psi.
a
fb bending stress on a mortar joint in a state of
combined compression, bending, and shear, psi.

fbo modulus of rupture of mortar joint, psi.

f ultimate uniaxial compressive strength of concrete.
c
fdt diagonal tensile strength of masonry.

fm' prism strength.

f maximum principal stress.
ma x
f normal stress on a cross-section.
n


xvi










Key to Symbols (Continued)


f external precompressive stress on a pier.

S average shear stress on a cross-section.
s

f apparent shear strength of mortar joint under
combined compression and shear, psi.

ft tensile strength of a material.

f
y
fyl precompression applied to brickwork.

fy2

II horizontal component of the ultimate load on pier.

H. weighting coefficients adopted in the Gauss
quadrature formula.

h height of a specimen.

[J] Jacobian matrix used for obtaining strain
transformation matrix for an isoparametric element.

KI,K2 structure stiffnesses.

[K] global stiffness matrix.

[k] element stiffness matrix.

1 length of a specimen.

M spandrel moment.

{N) interpolation functions.

n number of integration points used in the Gauss
quadrature formula.

P applied load on a specimen.

P ultimate load on a specimen.
u

{p} matrix of body forces in an element.

(Q} matrix of equivalent nodal forces corresponding
to "initial stresses".


xvii











Key to Symbols (Continued)

{R} external nodal point forces.

Ri total applied load during 'i'th load increment.

S elastic section modulus.

T applied horizontal load in racking test.

{T } strain transformation matrix.

{T } stress transformation matrix.

t thickness of a specimen; net thickness of a wall.

U. component of nodal force in the direction of
S 'u' displacement.

{u} matrix of displacements in the x-direction.

V base shear; vertical component of applied load.

Vi component of nodal force in the direction of
'v' displacement.

VpI load shared by pipe columns.

vm' shear strength of masonry.

v ultimate shear strength.

w unit weight of concrete, pcf.

X component of body force in an element in the
x-direction.

X1 horizontal distance from center of pier to point
of application of load.

{XI} number of unknowns in column 1.

X x-coordinate of node 'n' of an element.
n
x x-ccordinate of any point in an element.

Y component of body force in an element in the
y-direction.

y vertical distance of a cross-section of pier from
the point of application of load; y-coordinate of
any point in an element.


xviii










Key to Symbols (Continued)


a ratio of principal stress in orthogonal direction
to principal stress in direction considered;
direction of maximum principal stress at an
integration point; inclination of mortar joints to
global frame of reference.

0 shear retention factor.

y shear strain.

{AR} unbalanced nodal forces

{Ao.} incremental nodal displacements at node 'i'.

{AE'} incremental strains.

{A(} elastic incremental strains in the "initial stress"
method.

{Ac'} incremental stresses; true increment of stress
possible for the given strain in the "initial
stress" method.

{Ao} elastic incremental stresses in the "initial
stress" method.

{An"} initial stresses to be supported by equivalent
nodal forces

{6} nodal displacements.

c uniaxial strain.

{c( vector of strains at a point.

e ultimate uniaxial compressive strain of a material.
cu
{e } vector of initial strains.

ni local y-coordinate of node 'i'.

11 coefficient of friction between brick (block) and
mortar.

v Poisson's ratio of a material.

i. local x-coordinate of node 'i'.

a uniaxial stress at a point.


xix











Key to Symbols (Continued)


} vector of stresses at a point.

0,o uniaxial yield stress.

G normal stress at interface between block and
mortar.

o 0 ultimate strength of concrete plate in uniaxial
compression, psi.

{o } vector of residual stresses.

0 peak stress in biaxial compression, psi.

at tensile strength of a material.

E shear stress; shear stress at the interface between
block and mortar.

lim limiting bond shear strength of mortar.
11m















AbsLiact of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



AN INVESTIGATION OF THE STRENGTH
OF CONCRETE MASONRY SHEAR WALL STRUCTURES

By

Krishnaiyer Balachandran

August, 1974

Chairman: Dr. Morris W. Self
Major Department: Civil Engineering

The main objective of this investigation is to obtain

empirical equations to predict the shear capacity of nonre-

inforced concrete masonry elements. An analytical investi-

gation using a nonlinear finite element analysis and an ex-

perimental investigation were carried out for this purpose.

First, an experimental program was initiated to obtain

equations for predicting the strength of mortar joints under

combined compression, shear, and bending. The test speci-

mens were standard three-block prisms with three-eighths-inch

mortar joints. Precompression up to 300 psi was applied.

Based on test results, a circular interaction curve is pro-

posed for predicting the strength of mortar joints under

combined stresses.


xxi










In the second phase of the experimental program, the

shear strength of concrete masonry piers made with one-

fourth-scale model blocks was investigated. The main vari-

ables were the strengths of grout and mortar and the magni-

tude of external precompression. A relationship between

the shearing strength of a grouted pier and the correspond-

ing prism strength was established. Equations are proposed

for predicting the shearing strength of a nongrouted

concrete masonry pier.

A nonlinear finite element analysis, using the

isoparametric approach and higher order rectangular elements,

was developed to predict the behavior and collapse of con-

crete masonry elements. An incremental loading procedure

was adopted and failure was investigated at integration

points due to yielding, cracking, or crushing of the masonry

component. Also, criteria were developed to predict the

debonding of the mortar joints. The "initial stress"

approach was adopted to redistribute the released stresses,

due to cracking, to the surrounding elements. The initial

stiffness was used throughout each iterative cycle as well

as through all the load increments. Predictions of failure

patterns, collapse load, and deformations are compared to

experimental results.


xxii














CHAPTER 1

INTRODUCTION



1.1 History: Masonry construction is perhaps the oldest

building system employed by man as evidenced by the historic

remains of ancient temples in India and Egypt. These early

works evolved more from art than science and are character-

ized by their massiveness and quality craftsmanship. This

traditional masonry construction prevailed throughout the

United States in the nineteenth century and was culminated

by the construction of the Monadnock Building in Chicago,

Illinois, completed in 1891. This 16-story skyscraper has

exterior bearing walls varying in thickness from 12 inches

at the top story to 6 feet at the base.

Late in the nineteenth century, the concept of the

structural frame in structural steel or reinforced concrete

replaced masonry bearing wall construction. Masonry became

primarily an architectural product used in nonbearing parti-

tions and as a facing.

Expanded research in building methods and materials

early in the twentieth century, particularly with respect to

structural concrete, has resulted in renewed interest in

load-bearing masonry. Although a considerable amount of

masonry research has occurred since 1932 (43), there











exists little correlation among the various studies conducted

by governmental, promotional, and university research

agencies. Each study has of economic necessity been con-

strained within narrow bounds placed on the variables. For

this reason, recommendations based upon this research have

been purposely conservative. Much reliance has been placed

upon the results of the voluminous research and experience

with concrete and reinforced concrete; and research, design,

and construction procedures for reinforced masonry have ad-

vantageously followed those developed for reinforced concrete.

However, there are important differences in the behavior of

masonry and concrete that must be taken into consideration.


1.2 General Remarks: Concrete masonry walls are broadly

classified as either load-bearing or nonload-bearing and

further described in various ways such as either nonreinforced,

solid unit, or hollow unit.

The general behavior of high-rise,load-bearing structures

under gravity and lateral loads is the combined action of

floors, bearing walls, and shear walls. Floors transmit hori-

zontal forces by diaphragm action from the exterior walls to

the shear walls, which in most cases are also the bearing

walls. The floor system must be sufficiently rigid to serve

as a diaphragm, and connections must be adequate to transfer

these forces to the shear walls which carry them to the

foundation. The height to which the buildings can be











constructed depends upon the strength of the masonry

materials, the spacing of intersecting walls and floors, their

connection to each other,and the shape of the structure.

The design procedure includes an investigation of the

following (41)(20).

1) Bearing capacity: bearing stresses will generally

govern required block strength and wall thicknesses.

2) Stability against overturning: overturning resis-

tance to lateral loads depends upon the shape and mass of the

building. Shear walls that are also load-bearing walls are

the most effective structural elements for developing resis-

tance to overturning.

3) Shear resistance of walls: lateral load is trans-

mitted through the floors to those shear walls parallel to

the assumed direction of the lateral load. The percentage of

total lateral load carried by a shear wall is proportional to

this "relative rigidity" with respect to other participating

shear walls.

4) Flexural resistance of walls: lateral bending of

walls can be produced by wind loads on exterior walls, by

eccentricity of loading, and by insufficiently rigid floor

diaphragms and shear walls.

5) Floor-wall connections: finally, because the

strength and stability of the high-rise building depend upon

the interaction of the connecting floor and wall elements,

connections must be adequate.











As mentioned previously, shear walls are designed to

resist the effects of lateral forces acting on buildings.

The lateral forces are primarily due to wind or earthquake.

The performance requirements for shear walls under wind

loads are different than that for earthquakes (3). Walls

designed for wind forces have to meet both strength and

stiffness requirements. Walls designed for earthquakes must

also satisfy requirements of ductility and energy absorption,

damping characteristics and damage control, during several

cycles of inelastic deformation (1).

The behavior of shear walls is complicated by the

influence of boundary elements and multiple openings (14)(36).

Figures 1.1 and 1.2 [taken from reference (3)] present some

typical examples. Lateral loads are usually introduced into

shear walls through floor slabs framing into either one side

or both sides of the walls. As a result, the lateral loads

tend to be distributed across the width of the wall. Trans-

verse walls or columns are often located at the extreme

edges of the walls. They act with the wall, and usually

contain most of the flexural reinforcement resisting the

moment due to the lateral forces.

When a wall contains large openings, it can be

considered to be made up of a system of piers and spandrels.

Each individual pier or spandrel is, in effect, a shear wall

element, with a shear span approximately equal to one-half

of its height or length, respectively. In addition to shear,








5












FLOOR BEAMS .
OB SLABS 58>


SHEAS 'AAL'
WALL OR COLUMN 2s










Fig. 1.1. Shear wall with boundary
elements.



















SPANDRELS-- -'
PIERS--








Fig. 1.2. Elements of shear wall
with openings.











piers will also generally have tension or compression caused

by gravity and overturning forces as well as shrinkage,

creep, and differential settlement.

It is noted by the Joint ASCE-ACI Task Committee 426

on Shear and Diagonal Tension that the shear strength of a

wall is of interest only for shear span to depth ratios less

than 2, or for walls with a flanged cross-section (3).


1.3 Previous Investigations:

1.3.1 Strength of Mortar Joints: compared with the vast

number of tests reported on concentrically loaded walls with

the load applied vertically, little is known about the

strength of masonry walls with the load applied at different

inclinations to the horizontal joints. However, some test

results are reported. Benjamin and Williams (5) carried out

tests on shear couplets of two bricks bound together with a

mortar joint. Three different mortar types were tested with

watered, stiff mud, side-cut, vacuum-treated clay bricks.

The test results showed little or no influence of brick and

mortar compressive strengths on the couplet bond strengths

in tension and shear. The test results showed that the

relationship between the shear stress, fs (shear force

divided by wall area), and the normal stress, fn' could be

expressed in the form:


(1.1)


f = C + 1 f
s n











where p is the coefficient of friction between mortar and

brick and C is the initial bond strength, a constant.

Benjamin and Williams obtained a value of C = 150 psi and

p= 0.73. They also concluded that, up to a compressive

stress of approximately 650 psi, the shear strength

increases with the compressive stress. For higher compres-

sive stresses, the apparent shear stress still increases,

although the joint has already failed in shear. The addi-

tional strength is claimed to be due to friction.

Zelger (44) has reported tests on masonry specimens of

the type shown in Figure 1.3. Zelger obtained C = 2 kg/sq cm

and p = 0.5 in his tests. Yorulmaz and Sozen (44) tested

masonry specimens of model bricks 0.53" x 0.86" x 1.87" in

size. The results obtained from test specimens of the type

in Figure 1.3 gave C = 150 psi and p = 0.46.

Haller (22) adopting the test setup shown in Figure 1.4,

arrived at the following empirical relationships:



f = 35/f + 280 540 psi (1.2)
s n


fn < 200 psi



for normal quality masonry consisting of cored bricks (3300

psi to 6500 psi) and cement-lime-sand mortar (1225 psi).

If the Haller formula is approximated to linear

relationship, the following equation is obtained:








8


























Fig. 1.3. Type of test specimens used by
Zelger.














Averoge J
thickness
ot bd -.
joints: 0.47nch









Wh.ernorc 1-
gouges o
gougonh I - I
gauges length :
20 inch




6J 4 -rt,


Fig. 1.4. Test specimen adopted by Haller.











f = 50 + 0.88 f (1.3)
s n


f < 200 psi
n -


The tests of the type shown in Figure 1.3 give the

most representative values for shear strengths of the mortar

joints in masonry, since disturbances caused by the testing

machine platens, etc., are much less likely to occur in

this type of test compared with the couplet type tests.

From the limited number of tests mentioned, it seems

reasonable to assume that the bond or shear failure of a

mortar joint in brick masonry follows Equation (1.1) in a

range of approximately 2% to 15% of the compressive strength

of the masonry. C is of the order of 2% to 3% of the com-

pressive strength of masonry. However, since the couplet

tests indicate that the compressive strength of the mortar

has no influence on the bond strength, the shear strength

should be tested when high stresses are employed.

For compressive stresses lower than approximately 2%

of the compressive strength of the masonry, and for pure

tensile stresses, the shear strength falls below that calcu-

lated from Equation (1.1), as revealed by couplet tests and

model masonry tests. The pure tensile bond strength is

greatly influenced by workmanship and wetness of the bricks.

A suction rate of 20 g/min or less seems to give maximum

bond, although saturated bricks produce close to maximum bond.











For high compressive stresses, the apparent shear strength

again is lower than calculated from Equation (1.1).

Hedstrom (24) reports load tests of concrete masonry

walls with constant wall dimensions but with mortar bed

joints in 90, 45, and 0 inclination to the axial load,

which was applied parallel to the longer side of the walls.

The tensile bond strength obtained with the two types of

mortar was tested on masonry prisms of two blocks in

bending. A plot of bond shear strength vs. compressive

strength yielded C = 48.5 psi and p = 0.84 for M-type

mortar and C = 24 psi and p = 0.92 for S-type mortar. The

figures are supported by too few tests to be conclusive.

1.3.2 Racking Tests: the present standard racking test

described in ASTM E 72-68, Method of Conducting Strength

Tests of Panels for Building Construction, provides only a

relative measure of the shearing or diagonal tensile

resistance of a wall. Results of this test are consequently

valid only for comparison purposes and are not suggested for

determination of design values.

In this method of test (Figure 1.5), horizontal

movement of the wall specimen (8' x 8'),due to the horizon-

tal racking load at the top of one end, is prevented by a

stop block at the bottom of the other end. To counteract

rotation of the specimen due to this overturning couple,

tie rods are used near the loaded edge of the wall specimen.

Under racking load these rods superimpose an indeterminate










h


3 F4 IF - L = h = 8fl
3 FIF Floor or
foundation


Fig. 1.5. Arrangement of racking test and the force
distribution on the specimen.





---Jul-


//<\





TE SION COMPRESSION

Fig. 1.6. Test for diagonal tensile strength of
brickwork and stress distribution.
brickwork and stress tlistrihut ion.











compressive force which suppresses the critical diagonal

tensile stresses and increases the load required to rack

the specimen. A typical mode of failure is indicated.

The obtained apparent shear strength as calculated from

f = T/ld is usually of the order of 25 psi to 300 psi
s
under laboratory conditions.

For concrete masonry walls, the racking strength was

reported by Fishburn (18) to be 25 psi to 50 psi for

masonry walls having a compressive strength of 390 psi to

470 psi giving a racking strength of about 7% to 10% of

compressive strength.

1.3.3 Circular Shear Specimens (28): in these tests

(Figure 1.6), a 15" diameter specimen is tested in compres-

sion with the line of load at 450 to the bed joints. As

shown in Figure 1.6, the diametrical stresses are largely

tensile over the central 80% of the specimen. The tensile

stress is approximately constant for about 60% of the dia-

meter and may be calculated by the following equation:



S 2P (1.4)
t = Dt


where P equals load at rupture, in pounds, D equals the

diameter of the specimen, in inches, and t equals the thick-

ness of the specimen, in inches.












1.3.4 Square Shear Specimens (6)(16): in examining the

damage done during earthquakes, it was noted that cracks in

shear walls were frequently of a diagonal nature, so fre-

quently that they were called typical "X cracks" (Figure 1.7).

With this as a starting point, the theory was early recog-

nized that the force of quake working against the static

resistance of a building would produce a racking effect;

this in turn would be resisted by the diagonal strength of

the wall member. It was found that the "X" cracking devel-

oped in a diagonal tension test.

Photoelastic analysis through the use of polarized

stress panels was used to demonstrate the validity of this

theory (Figure 1.8). The stress distribution in the wall

panel was shown to be the same as in the diagonal test

panel. It was then decided that the proper test would

consist of breaking, by diagonal loading, 4' x 4' panels

incorporating desired variables (Figure 1.9). In this

method, the test results are susceptible to stress analysis.

In addition, they are more reproducible and thus more

reliable for comparison and design data purposes.

The square specimen is placed in the testing frame so

as to be loaded in compression along a diagonal, thus pro-

ducing a diagonal tension failure with the specimen split-

ting apart along the loaded diagonal. The shear strength,

































Fig. 1.7. Typical X-cracks in a wall damaged
by an earthquake.


Fig. 1.8. Fringe patterns obtained in a photoelastic
analysis of a model of a wall with an
opening and a square panel under diagonal
compression.





































Fig. 1.9. Diagonal tension test on a
square panel.


Loading Jacks


Loading Frame


Bearing Plates



Gap


Fig. 1.10. Test setup (schematic) adopted
by Meli and Reyes for testing
mortar joints under
compression and shear.











v ', is determined from the equation (6)(27):


0.707 F (1.5)
m tl


where F equals the diagonal compressive force or load, in

pounds, t equals the thickness of wall specimen, in inches,

and 1 equals the length of a side of a square specimen, in

inches.

1.3.5 Horizontally and Vertically Loaded Wall Without Frame:

the load carrying capacity of a wall subjected to a horizon-

tal load at one of the upper corners is governed mainly by

the shear and tensile strength of the bedjoints at the

foundation of the wall (44). By precompression, for example,

by dead load from slabs and walls above, the strength is in-

creased in a manner similar to that described for masonry

specimens loaded with an inclined load.

Murthy and Hendry (44) report "1/6-modal" tests on

three bay, one-story, shear walls, 0.669" thick, about 16"

in height and length. The bricks had an average strength

of 4421 psi and the cement-lime-sand mortar about 1200 psi.

The horizontal shear strength was tested for various addi-

tional loads up to 180 psi, and the following relationship

was established:


f = 30 + 0.5 f (1.6)
s n


f < 180 psi
n --











Benjamin and Williams (5) tested model walls, without

frames and without vertical loads, and found apparent shear

strengths of 15 psi to 30 psi.

1.3.6 Test on Small Masonry Assemblages: at the University

of Mexico, Meli and Reyes (39) conducted tests on small

assemblages for investigating the mechanical properties of

masonry. Three tests were found to be the most useful: a

small prism subjected to axial compression, a wallette under

diagonal compression, and a three unit assemblage subjected

to shearing of the joints. Results of the prism test were

related with the behavior of masonry walls under vertical

loads. The remaining two tests were related with the

behavior of walls under lateral loads. Tests were performed

on a large number of specimens built with commonly used

types of masonry units and mortars.

Based on test results, it was found that the prism with

height/thickness ratio of 4.0 gave satisfactory and uniform

index to the resistance to axial load of masonry.

Figure 1.10 shows the schematic test setup adopted for

the shearing tests on joints with precompression. The

results were expressed in the form of Equation (1.1) with

C = 1.8 kg/sq cm and p = 0.8 for concrete blocks with dif-

ferent types of mortar whose strengths varied from 151 kg/

sq cm to 43 kg/sq cm. Coefficient of friction was found to

be a very uniform property for the different types of bricks

and concrete blocks adopted. The values were approximately











0.7 in all the cases. However, the value of adhesion varied

depending on the type of brick and mortar. At low levels of

confinement, the results varied; however, uniformity in re-

sults was obtained with high level of precompression.

Figure 1.11 shows the different types of specimens

adopted for the diagonal compression tests. For each series

of specimens shown in Figure 1.11, four different types of

mortars and seven types of masonry units were used. For

each combination of materials, there were three specimens

of each type. The object of the series of the tests was to

study the effect of the variation of the height/width ratio

(h/l) of the panel and number of joints in the specimen on

the resistance of the assemblage. The results showed that

each type of specimen had a definite mode of failure inde-

pendent of the type of mortar used. In general, the failure

occurred by shearing along the joints for long specimens and

by diagonal tension for specimens with high h/l ratio. The

type of failure was not always perfectly defined. In many

cases, the crack crossed the joints and the blocks partially.

Qualitatively, it could be said that when the failure was by

diagonal tension, the resistance was relatively uniform for

similar specimens and did not depend much on the type of

mortar used. On the contrary, when the failure was by shear,

the dispersion of results was very high. It was found that

the resistance increased with increase in h/l ratio.














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However, the effect of this increment was of very little

influence when the failure was by diagonal tension and

very much noticeable when the failure was by shearing along

the joints. It might be due to the fact that the h/l ratio

controls the value of compression normal to the joints that

causes the effect of friction to be developed.

All the specimens considered in this investigation

were nongrouted. It was found that the strength in diagonal

tension was equal to the square root of the compressive

strength of the prism when the stresses were expressed in

kg/sq cm.

For the shear failure along the joints, a relation

similar to that of Polyakov (42) was proposed:



f = 0.8/(1 0.9 p h/1) (1.7)



1.3.7 Reinforced Concrete Masonry Walls in Shear: Figure

1.12 shows the steel arrangement of reinforced concrete

masonry walls tested by Converse (12). The basic mode of

failure was one of diagonal tension. Walls under group 'B'

showed an increase in strength of 38% over group 'A'. It

suggested that the increase in strength was nearly propor-

tional to the areas of additional steel, irrespective of

position. Due to the difference in number of bars, no

direct comparison could be made of the relative effect of

vertical and horizontal steel, but indications were that

they were equally effective.











Scrivener (48) confirmed the previous findings in his

tests. The objectives of his tests were to determine:

1) the pattern of behavior as the percentage of reinforcing

was increased, 2) the relative effectiveness of vertical

and horizontal reinforcing, and 3) the difference between

the behavior of walls where the vertical steel was periph-

eral and where the steel was distributed over the length of

the wall. The following conclusions were drawn from these

series of tests:

1) Vertical and horizontal reinforcing are equally

effective in producing satisfactory crack behavior and

failure loads.

2) Walls with evenly distributed reinforcing have a

later onset of severe cracking than walls where the rein-

forcement is concentrated in the wall periphery.

3) With a low percentage of reinforcing, failure

occurs soon after the onset of severe cracking. With higher

percentages of reinforcing, the failure load is much greater

than the load causing severe cracking.

4) Higher failure loads were obtained with walls with

higher percentages of reinforcing up to 0.3% of the gross

cross-sectional area of the wall. Above this percentage,

additional reinforcing had little effect on the failure

load. From the walls with the optimum (0.3%) or higher per-

centage of reinforcing, the ultimate horizontal shear stress











(ultimate load divided by the gross cross-sectional area

of the wall) was found to be 170 psi.

Confirmation of the last conclusion can be had from

the test results of Schneider (45), who found a maximum

effective quantity of reinforcement of 0.2%. In his tests,

a racking load only was applied, but sufficient peripheral

vertical reinforcement was placed in the walls to prevent

this steel being stressed beyond its yield point when sub-

jected to the tensile forces induced by the maximum over-

turning moment. Schneider's walls failed in shear with

the typical diagonal cracking. The difference between

Schneider's and Scrivener's test walls lies in the boundary

conditions on the vertical sides. Schneider also found

that, workmanship and reinforcement remaining the same, the

shear resistance of stack and running bond and stack bond

masonry block walls was about the same.

1.3.8 Effect of Wall Openings: openings in shear walls

are mainly due to doors, corridors and mechanical duct

space. When the opening is relatively small and spaced, at

least a distance equal to the size of the opening in each

direction, its influence on the behavior of the structure

is negligible (29). Figure 1.13 shows an elevation of a

typical shear wall in an apartment building using an 8"

concrete, flat plate slab construction. The opening shown

at the center indicates the corridor at each floor. In
































Fig. 1.13, Continuous opening in a
shear wall.


Fig. 1.14. Staggered opening in a
shear wall.











apartment buildings, the opening would normally be from

top of the floor to bottom of the floor above. In apart-

ment buildings where the architectural planning frequently

permits the shear wall to extend from one face of the

building to the other, openings such as shown in Figure

1.13 limit the full utilization of the entire shear wall as

a unit. The connecting slab at each opening is relatively

very flexible. As a result, the shear wall acts as two

individual shear walls on either side of the corridor

opening. Although for medium height buildings, this inef-

ficiency does not seriously affect the economy of the

entire structure, for heights above 40 stories, its effect

on overall economy becomes significant. As a solution to

this problem, Khan (29) proposes staggering of such open-

ings at alternate floors in order to maintain the struc-

tural continuity of the entire shear wall. Figure 1.14

illustrates the proposed arrangement.

In office buildings the requirement for mechanical

duct space under the floor slab makes the problem of open-

ings different from that in the apartment buildings. A

hung ceiling is almost always necessary. The door opening

size generally allows a 2 ft to 5 ft connecting beam over

each opening. The proper analysis and design of the con-

necting beam is important because the beam not only con-

nects the adjacent parts of a shear wall for monolithic

action, but also redistributes loads in different parts of











the shear wall. Girijavallabhan (21), on the basis of an

analysis using the Finite Element Method, found that one

of the most influencing factors on the distribution of

stresses and deformations in the shear wall was the stiff-

ness of the lintel beam. He varied the depth of the lin-

tel beam and studied the influence of the variation on the

overall behavior of the shear wall.

Kokinopoulos (30) conducted a photoelastic analysis on

models of single story walls with openings to study the

effect of size of opening on the stress distribution in

walls. Schneider (46) conducted full scale tests on piers

in a shear wall with openings. This is the only experi-

mental investigation on this problem which utilized full

scale tests. This investigation is described in the next

subsection.

1.3.9 Shear in Concrete Masonry Piers: this investigation

was carried out to estimate the capacity of concrete masonry

piers, functioning within the confines of a shear wall in a

building, to resist lateral load effects. To simulate as

nearly as possible conditions that occur in an actual wall,

such as degree of restraint, amount of reinforcing, manner

of vertical load imposition, and magnitude of secondary

stresses, the pier was considered along with the wall around

it (Figure 1.15)'. The fully restrained configuration was

either 10' 8" or 11' 4" high. The cantilever pier was either




























I ti


I,


PANEL 'FREEBODY"
SHEAR TLS!


Fig. 1.15. Forces acting on a pier
element in a wall with
opening.


DIACOIGAt LOAD FRAME
(PIER DI-TAILS VARY)


Fig. 1.16. Test setup adopted by
Schneider for full scale
tests on piers.


--LJ------L-


6


--











7' 4" high and 8' 0" wide or 10' 0" high and 10' 8" wide.

Also tested was a set of 48" square concrete masonry assem-

blies. A diagonal loading frame was used to apply the

loading (Figure 1.16). Pipe columns were used to maintain

the geometry of the openings.

The important variables considered were:

1) a/D ratio, where a is the distance from the point

of inflection to the spandrel restraint, and D, the overall

pier depth.

2) Amount of web reinforcement (both horizontal and

vertical).

3) Amount of jamb reinforcement.

4) External axial compressive stress.

5) Nongrouted panel behavior.

The average strength of blocks used varied from 1338

psi to 2962 psi. The 28-day mortar strength varied from

2487 psi to 5116 psi. The strength of grout prisms varied

from 1789 psi to 3414 psi. Reinforcing steel conforming

to ASTM A 15, had a yield strength of 55,000 psi and ulti-

mate tensile strength of 80,000 psi.

The following are the main findings of this investigation:

1) The shear strength increased with a decrease in the

a/D ratio, and this rate of increase jumped sharply below an

a/D ratio of 0.5:1.

The very consistency of the test results throughout the

range of a/D ratios selected for analysis suggested the











following relationships for average ultimate shear stress

of a pier contained within a shear wall, where web rein-

forcement is not provided:


M/VD (a/D)

Fixed Pier Elements:

0.10:1 < M/VD < 0.50:1

0.50:1 < M/VD < 1.50:1

1.50:1 < M/VD

Cantilever Pier Elements:

1.0:1 < M/VD < 3:1

3.0:1 < M/VD


ULTIMATE MASONRY SHEAR STRESS,
Vu, psi


V/tD = 310 350 M/VD

V/tD = 152.5 35 M/VD

V/tD = 100 psi



V/tD = 95 15 M/VD

V/tD = 50 psi


where M equals spandrel moment, V equals base shear, D

equals overall pier depth, a equals distance from the point

of inflection in the span of the pier to the fixed end, and

t equals net thickness of wall.

2) The presence of adequate horizontal web

reinforcement materially increased the shear resistance of

the pier.

The following relationships between the M/VD ratio and

ultimate shear stress were proposed for piers with horizontal

web reinforcement.











ULTIMATE MASONRY SHEAR STRESS
WITH ADEQUATE WEB REINFORCEMENT,
M/VD (a/D) vu, psi

Fixed Pier Elements:

0.10:1 < M/VD < 0.50:1 V/tD = 347.5 225 M/VD

0.50:1 < M/VD < 1.50:1 V/tD = 290 110 M/VD

1.50:1 < M/VD < 2.00:1 V/tD = 200 50 M/VD

2.00:1 < M/VD V/tD = 100 psi



3) Vertical steel did not seem to function effectively

as web reinforcement.

4) Assuming that enough jamb steel was present to

resist the end moments, any further increase did not alter

the pier resistance appreciably.

5) The existence of a bedjoint fracture at a foundation

did not seem to impair the ability of the panel to resist

lateral loads. However, if a bedjoint crack occurred at the

center of a square panel, where tensile stresses are maximum,

its shear resistance was drastically reduced.

6) The energy absorbing ability of an adequately rein-

forced masonry pier was well demonstrated. As the shape of

the load deflection curves indicated, these piers were able

to absorb a great deal of inelastic strain energy without

collapsing or even spelling seriously.

7) Concrete masonry, if properly reinforced, exhibits

a tendency toward a ductile behavior throughout the loading











sequence. It can sustain significant proportions of the

ultimate load well into the inelastic regions (beyond the

first significant crack) while undergoing rather large

lateral deflections. It also exhibits effective dampening

characteristics, especially after cracking.

8) On the basis of defining ductility as the ratio

of the total deflection experienced to the deflection at

the first shear crack, which was assumed to be the incep-

tion of inelastic deformation, the ductility factor

exceeded two, which is considered a desirable level.

1.3.10 Strength of Masonry under Combined Compression and

Shear: Sinha and Hendry (50) propose that brickwork sub-

jected to combined compression and shear exhibits two dis-

tinct types of failure:

1) Shear failure at the brick/mortar interface. The

shear strength consists of initial bond shear and the resis-

tance, proportional to the normal stress, due to friction

between brick and mortar.

2) Diagonal tensile cracking through bricks and mortar

governed by constant maximum tensile stress or strain.

On the basis of tests on circular shear specimens,

Sinha and Hendry found the diagonal tensile strength of

brickwork to be:


f = 2.0 f
t m


(1.8)











Let f equal precompression applied to brickwork and

fs equal shear stress. If it is assumed that failure is

determined at a certain stage by the criterion of maximum

tensile stress, then:


f
ft = /f 2/4 + f 2 = constant (1.9)
y s


For failure:



f > f
fs- y


It is assumed that the above condition will be fulfilled by

two values of f : f y and fy2. Between the precompressive

stresses f y and f 2 failure of the structure will occur by

attaining maximum tensile strength. Below and above this

range, failure will be governed by shear at the brick/mortar

interface. Precompression above f 2 will suppress the

inherent failure due to diagonal tension and modify its

value. At very high precompression values, the failure of

the brickwork will take place in compression.

Since fs = C + P fy, where C is the initial bond shear

strength between brick and mortar,



ft = fy2/4 + (C + 11 fy )2 fy/2 (1.10)











When fs = P fy2,



S= f2/4 + ( f 2)2 f2/2 (1.11)


Knowing ft, C and V, f y and f 2 can be calculated. Thus,

the ultimate shear strength may be calculated from the

following formulae:



f = C + p f (1.12)



for p fy < f 1, and,



ft = f 2/4 + f 2 fy/2 (1.13)


for f f < f 2 and,



f = I f (1.14)



for f 2 < f < compressive strength of brickwork.



However, in a recent study, Smith et al. (51) have

concluded that the diagonal tensile strength of brickwork

is approximately equal to the tensile strength of brickwork

or mortar, whichever is weaker. This conclusion was based

on an analysis of a masonry circular shear specimen using

the Finite Element Method supported by experimental data.











1.4 Objectives and Scope of Present Investigation: A

survey of the available literature revealed a need for more

elaborate research on shear strength of concrete masonry

walls with openings. To meet this objective, an experimen-

tal and an analytical investigation is attempted in this

dissertation. In the experimental investigation, it was

decided to adopt the test specimen proposed by Schneider (46).

Thus, the main objective of the experimental investigation

was to obtain empirical equations to predict the shear capa-

city of grouted and nongrouted piers without reinforcement.

Since the effect of various types of configurations and

reinforcement had already been established, it was decided

to restrict the investigation to one particular configuration.

The main variables considered for grouted piers were the

grout and mortar strengths; for the nongrouted piers, the

effect of external precompression normal to bedjoints was

treated as the main test parameter for different types of

mortar adopted.

Since the strength of mortar joints is a main factor

determining the behavior of a nongrouted masonry element,

an extensive study was initiated to obtain equations for

predicting the strength of mortar joints under combined

compression, bending and shear. This investigation is

described in Chapter 3.











A full-scale testing of piers was not possible

because of limitations of capacity of testing machines,

space, and cost. The present investigation on piers was

restricted to 1/4-size models. Chapters 4 and 5 describe

the model tests on piers.

While investigating a complex phenomenon such as the

behavior of masonry, if a suitable analytical model could

be proposed, it would facilitate understanding the stress

distribution in the structure more thoroughly. Such a

model was attempted using the Finite Element Method. The

model chosen was capable of predicting the different failure

modes associated with masonry and a nonlinear finite element

analysis was adopted accordingly to determine the ultimate

load and failure pattern. The analytical results were com-

pared with experimental ones. The analytical investigation

is described in Chapters 6 through 8.















CHAPTER 2

EQUIPMENT, MATERIALS AND TESTING TECHNIQUES



2.1 Testing Machines and Other Equipment: The Civil

Engineering Laboratory is equipped with a hydraulic press

of 300,000 lb capacity and a mechanical press of 160,000

lb capacity. The clearance of these two machines allowed

good observations of all sides of the specimen being

tested. For testing the model reinforcement, the 10,000

lb capacity, Instron Machine, Model TTC, in the department

of Metallurgical Engineering was used. The machine was

provided with suitable gripping devices for clamping small

test specimens and an automatic recorder for plotting the

load-extension curves.

The investigation on the strength of mortar joints

was carried out in the 300,000 lb hydraulic press. The

higher clearance and lower load ranges required for the

model tests determined the use of the 160,000 lb mechanical

press for testing model piers.

Sieves, mechanical shakers, and balances were available

for analysis of sand.

An electric rotary mixer of 5 cu ft capacity was used

in mixing mortars for building 3-block prisms used for deter-

mining the strength of mortar joints under combined stresses.











The same mixer was also used for mixing cement-sand mortar

for making spandrels for piers. A standard flow table,

standard molds for mortar cubes, paper molds for mortar

cylinders, and different size rods were used for mortar and

grout control.

A large moist room was used for storage of mortar

cubes and cylinders, and sufficient storage room was avail-

able for the masonry prisms and model specimens.

A 6" diameter brass disc (normally used for capping

concrete cylinders), together with four 1/4" x 1/4" brass

bars, formed a mold for the sulfur caps of the model con-

crete blocks and prisms.

Dial gages with a least count of 0.001" were used for

measuring deflection. They were mounted on magnetic stands

for easy removal.

The electrical strain gages used were BLH's SR-4 fixed

on the test surface with Duco cement. The strain indicator

was a portable Baldwin Type N. The strain gages were wired

to the indicator through a switch selector.


2.2 Concrete Blocks: The concrete blocks used for the first

investigation had nominal dimensions of 8" x 8" x 16". The

net area of a block based on the average of five specimens

was 61.4 sq in. Selected blocks were capped with sulfur and

tested according to ASTM C-90 and C-140. The average com-

pressive strength based on net area was 6500 psi. The ini-

tial rate of absorption (IRA) of the block, according to











ASTM C-67, is measured as the amount of water initially

absorbed by a dry unit when it is partially immersed in

water to a depth of 1/8" for a period of one minute. IRA

is measured in grams per minute per 30 square inches. The

test was conducted in the following manner.

Four steel bars, 1/4" x 1/4" in cross-section and 4"

long, were provided with needles 1/8" high. A steel pan,

which area was much larger than the gross area of the con-

crete block, was chosen and placed on a level surface. The

steel bars were positioned on the pan in such a manner that

the concrete block could rest on them. Water was allowed

to stand in the pan till the needle points were just

immersed. The previously weighed block was placed in posi-

tion over the steel bars, and the water supply was continued

to cope with the absorption of the block. After one minute,

the block was removed, the immersed surface wiped, and the

block reweighed. The initial rate of absorption of the

blocks varied between 12 g to 17 g/min/30 sq in.

An indirect tension test was conducted to find the

tensile strength of the block (49). Two test methods were

devised for splitting hollow concrete block. The first

method, shown in Figures 2.1(a) and 2.1(b), was arranged so

that the block could be split twice. The load was applied

through hexagonal bars with 3/4" flats, first through one

cell and then through the other cell of the block. The

second method, shown in Figure 2.1(c), was arranged to load





asf











both cells simultaneously. Round bars of 1-3/8" diameter

were used to distribute the load in this test. Usually

only one split occurred as is shown in Figure 2.1(d). The

results of the tests are given in reference (49). The

indirect tensile strength of the block was calculated using

the relation:


2P
f (2.1)
t TA


where P is the splitting load and A the sectional area of

split. In the range of the block strengths tested, it

appears that the split tensile strength is approximately

five times the square root of the compressive strength as

determined by the standard block compression test. For

the blocks used in this investigation, the indirect tensile

strength was found to be 405 psi.


2.3 Mortar: The cements and sand were provided by local

suppliers in Gainesville, Florida. The cements were manu-

factured by Florida Portland Cement. Portland Cement Type

I and Masonry Cement were used in the mortar mixes in

accordance with ASTM C-270-68. The granulometry of the

sand is shown in Figure 2.2. For the first investigation,

two types of mortars were used. The following are their

proportions by volume.






40












100



80



60
\




40



20




16 30 50 60 80 100 140 200
(l.O-~n) (0. LTm)
SIEVE No.(OPENING SIZE)


Fig. 2.2. Sieve analysis of sand for masonry mortar.











PC MC Sand

Type I 1 1 4.5

Type II 1 1 6



An initial rate of flow of about 100% was adopted. Two-

inch cubes were molded and tested according to ASTM C-270.

The average compressive strength of Type I mortar was 1948

psi and that of Type II 917 psi.


2.4 Model Concrete Blocks: The model concrete blocks were

provided by the National Concrete Masonry Association,

Arlington, Virginia. They were modelled to be one-fourth

the size of the full block of nominal dimensions 8" x 8"

x 16". Thus, the model block had nominal dimensions of 2"

x 2" x 4". A typical block is shown in Figure 2.3. The

average length of the block was 3.9", width 1.9", and

height 1.85". The net area, based on an average of six

specimens, was 4.16 sq in. The model blocks, capped with

0.15" thick sulfur capping, were tested in axial compression.

The average of thirteen tests yielded a compressive strength

of 2688 psi based on net area. The coefficient of variation

was 20.15%.

The absorption of the model block was 11.98%. It was

difficult to measure the initial rate of absorption for the

model blocks because 1) their rate of absorption was quite

high, and 2) a suitable depth of immersion of surface could

not be defined for models.


1





































Fig. 2.3. Model concrete block


Fig. 2.4. Model reinforcement (0.147" dia.).











The tensile strength of the block could not be

determined by an indirect tension test because of the un-

certainties involved in choosing the size of splitting

bars for models. Also, a suitable testing machine was not

available. A value equal to five times the square root of

the compressive strength of the block was assumed.

In order to obtain the stress-strain curve in

compression, two SR-4 gages were mounted centrally, one on

each longitudinal side. The gage length was 0.2". The

stress-strain curve obtained is shown in Figure 2.5.


2.5 Model Reinforcement: Number 2 bars of 40 ksi grade

steel were used for main reinforcement in spandrel beams of

model piers. For vertical and shear reinforcements, 0.147"

diameter, high strength Duro-Wall bars were used. A typical

bar is shown in Figure 2.4. The bar had minute depressions

0.3" long and alternate projections 0.1" long. The yield

and ultimate strengths of the bar were, respectively, 68 ksi

and 75 ksi. A typical stress-strain curve is shown in

Figure 2.6.


2.6 Model Mortar: Based on trial mixes, the proper grade

of sand for modelling Type I and Type II mortars was arrived

at. The sand, of gradation shown in Figure 2.2, was sieved

through a set of sieves (nos. 8, 16, 30, 50, 100, and 200,

in that order). Trial mixes were made with the sands re-

tained on sieves nos. 50, 100, and 200. It was found






















3600.





3000






a2400
z

w


1800





1200






600







0 300 600 900 1200 1500

STRAIN ( x 10"6 IN./IN. )


Fig. 2.5. Stress-strain curve for model concrete block.










fu = 75.78

















48.32


Diameter of bar: 0.147"

Gage Length: 3.25"


0.04


0.06


0.08


STRAIN ( IN./IN. )


Fig. 2.6. Stress-strain curve for model reinforcement.


fy = 68.35


0.02










that for the same water-cement ratio and proportions of

ingredients, the strengths of mortar obtained, using the

sand retained in no. 100 sieve, compared favorably with

those of Type I or Type II, as the case may be. Hence,

this grade was chosen as the model sand. No attempt was

made to model cements. An initial flow of 120% was adopted.

Compressive strength of the mortar was determined by testing

standard 2" cubes. The tensile strength was obtained by

splitting cylinders 3" in diameter and 6" long. The model

mortar properties are summarized in Table 2.1. Plates,

5.75" x 5.75" x 0.625", made of the different types of

mortar and cured in air, were tested in uniaxial compression.

The plate compression strength was used in the analytical

investigation described in Chapter 8. The stress-strain

curves for the two types of mortars obtained on the basis of

tests on 3" x 6" cylinders are given in Figure 2.7.


2.7 Model Grout Mixes: No gravel could be used in model

grout because of difficulties in obtaining proper compaction

due to the small size of the cells. Hence, the model grout

consisted of only cement and sand. Standard 2" cubes molded

in standard molds and cured in air were used for measuring

the compressive strength of the grout. Due to the uneven

surfaces obtained for cubes molded by using the concrete

blocks as molds, the test results on those cubes were not

satisfactory. Plates, 5.75" x 5.75" x 0.625", were tested

in uniaxial compression. Their compressive strengths were












2800 -





MS
2400 -






2000






1600


z

MW
LI
S1200
LIn





800 -






400







0 800 1600 2400 3200

STRAIN ( x .0 6 IN./IN. )


Fig. 2.7. Stress-strain curve for model mortar.















TABLE 2.1

PROPERTIES OF MODEL MORTAR AND GROUT


Proportions by
Volume


Initial
Rate of
Flow


28-day Strength
Cube Split
Plate Comp. Cylr.


Type PC MC Sand % psi psi psi

Mortar: MS 1 1 4.5* 120 656 1695 200

MW 1 1 6 120 485 905 135

Grout: GW 1 5 +450 570 75

GM 1 4 +760 800 205

GS 1 3 ** 1000 1850 322

Note: Gradation of sand: passing through sieve no. 50 but
retained on sieve no. 100.
+ Gradation of sand: passing through sieve no. 30 but
retained on sieve no. 50.
** Gradation of sand: as shown in Figure 2.2.






49






2100

GS


1800



10 GM
1500

//


S1200




900

/


600 GW




300 /





0 300 600 900 1200 1500
STRAIN ( 106 IN/IN. )

Fig. 2.8. Stress-strain curve for model grout.

















3600






3000






2400






n 1800




0n




Q- /


















Fig. 2.9. Stress-strain curve for spandrel mortar.











required for use in analysis later. The indirect tensile

strength was obtained by splitting cylinders 3" in diameter

and 6" long. The properties of grout mixes adopted are

summarized in Table 2.1. For grout types GW and GM, the

sand used was of such a grade it passed through sieve no.

30, but was retained on sieve no. 50. For type GS, the

sand used for mortars Type I and Type II was adopted.

Initially, the required amount of water was determined by

trial for each type so that the grout could easily be poured

in the cells without separation of its components. The

stress-strain curves obtained using 3" x 6" cylinders are

shown in Figure 2.8.


2.8 Mortar Mix for Spandrel: A mortar mix of the following

proportions by weight was used in forming the spandrel of

the pier specimen used in model tests described in Chapter 4:

Portland Cement:Sand (river sand used in concrete mixes) = 1:3.

A water-cement ratio of 0.55 by weight was adopted. The

compressive strength of the mix was 3830 psi and the tensile

strength 400 psi. Compression tests on a plate of 5.75" x

5.75" x 0.625" yielded 2300 psi. The stress-strain curve

obtained by testing 3" x 6" cylinders under uniaxial com-

pression is shown in Figure 2.9.















CHAPTER 3

STRENGTH OF MORTAR JOINTS UNDER COMBINED STRESSES



3.1 Scope: This study was designed to investigate the

influence of precompression upon the shear and flexural

tensile strengths of mortar joints in concrete block

walls. First, the strength of the joint is studied under

a state of pure shear. Secondly, this is followed by a

study of pure bending. In the third phase, the strength

of the joint is studied under combined bending and shear

for a known amount of precompression. Combining the

above, the study is directed toward obtaining interaction

diagrams that can be used to predict behavior under com-

bined loading.

The structural bond between mortar and units is an

important factor in the structural behavior of masonry

walls where the masonry is subjected to forces which pro-

duce tensile and/or shearing stresses in the joints.

Factors which seem to influence the bond of masonry mor-

tars are (13)(25): 1) composition, 2) suction rate (IRA),

3) initial moisture content of the block, 4) compressive

strength, 5) air content, 6) initial flow of mortar, and

7) curing of specimens. Shear bond may be considerably

increased by the presence of compressive stress normal to

the shearing force.











In the present investigation, only the mortar

composition and strength were considered as variables.

Other factors such as suction rate, initial flow, block

characteristics and curing procedures were standardized

and held constant.


3.2 Test Specimens: Test specimens were standard 3-block

prisms with 3/8" mortar joints. All specimens were air-

cured under laboratory conditions. The initial rate of

absorption of the blocks varied between 12g to 17 g/min/

30 sq in. The net area of a block, based on the average

of five specimens, was 61.4 sq in. Since the blocks were

fully bedded, this value was taken as the area of a mor-

tar joint. Type M mortar was used with two compositions

The properties of mortars used are summarized in Table 3.1.


3.3 Strength of Mortar Joints under Compression and Shear:

A simple method was developed for applying shear to the

joints while a constant uniform compressive stress was

maintained across the joints. The specimens were supported

and loaded in such a way that the joints were at the points

of contraflexure. The testing arrangement adopted by Base

(4) was used with certain modifications. The test setup

adopted is shown schematically in Figure 3.1 and positioned

in the hydraulic press in Figure 3.2. The axial force

across the section was applied through steel rods and was

varied by tightening nuts at the threaded ends. The amount
















TABLE 3.1

PROPERTIES OF MORTAR


Proportion by
Mortar Volume


Initial
Rate of
Flow


28-day Strength
Cube Split
Comp. Cylr.


Specimens Type PC MC Sand % psi psi

PSM 1-12 II 1 1 6 90 864 172

PSM 13-25 II 1 1 6 103 932 198

PSM 26-37 I 1 1 4.5 96 2138 290

PSM 39-41 II 1 1 6 110 956

PSM 42-44 I 1 1 4.5 100 1758




























1"-thick bearing plate

3/4" threaded rods

Celotex Board


points of contrMa- A
flexure at joints





\ + / BENDI NG MOMENT DIAGRAM


Fig. 3.1. Setup for studying the strength of

mortar under pure shear.


Test Specimen












































Fig. 3.2. Test setup for finding the strength of mortar joints
under combined compression and shear.


IIT-' A~bh&~d~red~1I


Fig. 3.3. Shear failure through mortar joint.











of prestress developed in the rods is found by measuring

the strains with electrical strain gages. On each rod,

two strain gages were mounted diametrically opposite to

each other and connected in series to compensate for

bending effects.

Table 3.2 presents the summary of test results for

the low strength mortar and Table 3.3 for the high strength

mortar. For the low strength mortar, at precompressions

up to 220 psi, bond failures were observed; but at a pre-

compression of 300 psi, shear failure through the mortar

frequently occurred. Figure 3.3 shows an example of shear

failure through the joint. However, for the high strength

mortar (within the range of precompression adopted), the

failure pattern was always one of bond. Testing beyond

the range of precompression (300 psi for the high strength

mortar) was not possible due to flexural failure of the

concrete block.

Figure 3.4 shows the plot between precompression and

the shearing strength of mortar joints. It is evident

that the effect of precompression is to increase the

shearing strength of the joint considerably. It can also

be observed that a higher strength mortar does not appre-

ciably increase the shear strength. This statement cannot

be generalized because, within the range of precompression

applied thus far in this investigation, bond failures were

usually observed. It is quite possible to have an increased




















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S/

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o= 0.606 fo + 54
0 /


A MEAN VALUES


/0
/ A 1 :1 :1MOR T AR

0 1:1:6 MORIAR





PERMISSIBLE SHEAR STRESS


PRECOMPRESSION, PSI


Fig. 3.4. Effect of precompression on the shearing
strength of mortar joints.


fo = 0.6641


I











shear strength due to increase in strength of mortar at

higher precompressions, because the failure would likely

be due to shear failure of the mortar.

Using the method of least squares, the best-fit curve

for the observed data was found to plot as straight lines

with the following equations:



f = 0.606 f + 34 (3.1)
so a


for 1:1:6 mortar, and,



f = 0.641 f + 54 (3.2)
so a


for 1:1:4.5 mortar.

The above equations may be used for predicting the

shearing strength of mortar joints with a precompression

up to 300 psi for Type M mortar when blocks having an IRA

of 12 g to 17 g/min/30 sq in are used.

The specifications (2) limit the allowable shearing

stress to 34 psi for Type M mortar, irrespective of the

strength of mortar or level of precompression. Test re-

sults to date indicate clearly that the specifications are

conservative.



















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(f) U) U











3.4 Strength of Mortar Joints under Compression and

Bending: The test setup shown in Figure 3.1 was modified

to produce bending in the specimen with flexural stresses

acting normal to the bedjoints. The load corresponding

to the first crack was taken as the failure load since

beyond the initial failure, the load could have been shared

by the prestressing rods. Table 3.4 presents the results

of the tests. The maximum bending moment corresponding

to the failure load, when divided by the section modulus

of the joint, yielded the value of modulus of rupture

shown in Table 3.4. Adopting the cross-section of mortar

joint shown in Figure 3.5, the value of section modulus

corresponding to the extreme fiber was obtained as 117 cu in.

The results are plotted in Figure 3.6. Failure at the joint

was precipitated by a break in bond between the mortar and

the blocks.

The modulus of rupture appears to increase linearly

with precompression. In addition, the influence of precom-

pression upon the modulus of rupture is significant with

high strength mortar. The following empirical relations

are proposed:



fbo = 1.250 f + 27 (3.3)
bo a


for 1:1:6 mortar, and,














1 .25"


1.25" 1 .25"-


HO L LOW





15.6" T1


Fig. 3.5. Cross-section of a mortar joint.











560




480




00oo


/
//\
/ f

o fbo 1.25a + 27


o- 1:1:6 MORTAR

A 1:1: 4 MORTAR


150
PRECOMPRESSION, PSI


Fig. 3.6. Effect of precompression on the flexural
tensile strength of mortar joints.


f o = 1.725


520




240


16o




80


































4 )

-r-
0
*-I







ca
41







0








o-
0









on
4-J









-u




C6








-'-4
(0
















ro
-o
CO
C)








Q)
























r- L- r- r- r t

m n m CV) iv Ln Lf



o o o a0 I I
o o o o v<
N N N N 'N CN4 N



rn <3< a) CN r m) CN
CN Lfn C I n (n CN (1)




e m cc 0 o oD r m
o -i O m m m


Ur)







H

z




o




O


U



H
E z


0









H
0




E
CQ

a:


O *
O H




0 -
1fnU)
















4a 0
4-4 124











04
04-) %

UE- )


4J



4J -


U)

al( Q) *H

X 4-J 0



(n


I-T %D D D 00
%D in) in in) in
a) a a a r^'
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0 0 0 0 0 0 0
0 0 0 0 0 0 0
c' m 14 m CN


H H H
H H
H


> H H
H H H
H














S- 1:1:6 MORTAR

A- 1:1:1 MORTAR


fb / fo


Fig. 3.8. Interaction of bending and shear
under constant precompression.


2
<--











bo = 1.725 f + 42 (3.4)



for 1:1:4.5 mortar.

Here, also, the specifications are conservative in

limiting the allowable stress to 23 psi.


3.5 Combined Compression, Bending, and Shear: Various

test arrangements were devised to produce several combina-

tions of bending and shear under a constant precompression

of 300 psi. These testing arrangements are shown schemat-

ically in Figure 3.7, and the results are summarized in

Table 3.5. Knowing the mean value of modulus of rupture

at a precompression of 300 psi (fbo), also the shear strength

(fso) without flexure, and the combined bending and shearing

stresses (fb and fs), the values of fb/fbo and fs /fso can be

calculated and plotted to provide the unit interaction curve

shown in Figure 3.8. It is anticipated that this curve is

one from a family of curves that will be generated by vary-

ing the precompression in an expanded program of testing.

Thus, the flexural and shearing stresses in a mortar joint

under combined loading can be assumed to follow the equation:


+ ( = 1 (3.5)
so bo















CHAPTER 4

MODEL TESTS OF CONCRETE MASONRY PIERS



4.1 Selection of Model: The problem under investigation

consists of determining the stress distribution in a con-

crete masonry shear wall, particularly in the region be-

tween openings called piers. Even if models were used,

it is not economical to fabricate a model for a multiple

story wall with a large number of openings. Schneider (46)

conducted a photoelastic analysis on plastic models with

configurations as shown in Figure 4.1. The loads were

applied either diagonally or horizontally for all config-

urations except in the case of multiple pier models where

the load was applied in a manner simulating the way in

which a roof diaphragm would load a shear wall. A simi-

larity in fringe patterns was found to exist between the

model walls containing several piers and a diagonally

loaded single pier. Accordingly, the test specimen was

chosen as described in subsection 1.3.9 of Chapter 1.

In this investigation, a linear plane stress finite

element analysis is adopted in lieu of a photoelastic

analysis to verify the above findings and also to check

the effect of pipe columns that have been used to maintain

the geometry of the openings. The configurations chosen




















o/r) *-- 1.1
S!1 ', :l'. I0 "i' -1n.P

c-Di [1]
11Ed [-:I


7.1] L:]


IF

o/D -- .i



N a/D .2=
I'U.LIl.TIF i'5l'S -- SlN:- L. S'I*' Y


,..II' IPLE f'!. 'S -- ; t .i ; h." '


Fig. 4.1. Photoelastic model configurations
chosen by Schneider.











for analysis and the finite element idealization are

shown in Figures 4.2 through 4.5. Figure 4.4 shows the

pier in a story with openings and walls on either side of

it, but loaded diagonally; Figure 4.5 shows the configu-

ration adopted by Schneider. In this case, the pipe

columns are idealized as an equivalent rectangular element.

The equivalent modulus of elasticity of the element is

calculated by equating the axial rigidities of the actual

pipe column with that of the idealized element. In a

photoelastic analysis, the fringe patterns represent the

lines joining the points of constant maximum shear stress,

also called isoshear lines. In the analysis, maximum

shear stresses are computed at centroids of all elements.

The contour lines for these values represent the isoshear

lines. The isoshear lines are plotted for all the piers

investigated and these are shown in Figures 4.6 through

4.11. It is evident that the fringe patterns in all the

above cases are very similar and this confirms the method

of loading adopted in a single pier to simulate the actual

loading conditions a pier in a wall is subjected to.

To check the effect of substituting pipe columns for

end piers (Figure 4.4), the modulus of elasticity of the

pipe column elements was arbitrarily increased by 100%.

However, the corresponding changes in the maximum stresses

in the pier were less than 1% of the previous values.


I















0.5P


I I


I I


I I


Fig. 4.2. Finite element idealization for a
shear wall with openings.


0.5P







P







P


I "- 1- 12" -I 12" I 12" 6"1 I


0.5P





































Ckj






7t,7 ,f7


i~, I 3 1 23'


I 12" I 1 2"


I_ 12"_ I 6"'


' I-. I PH 11 1


Fig. 4.3. Finite element idealization for a
multiple pier shear wall.


O.5P








P


I 1


!






























11[ 9 11 L- 9


t) o
a v



a)
Q)
04-i .

0 0
-H 0H

4J
ca
o c





4-i
~Jw
co
4) to
i-l c0








0)




---
4.J



4C4
e c

rI
(U 0

&,







































-6" 6 -


Fig. 4.5. Finite element idealization for the test
specimen adopted by Schneider.


12"11P- I 6" 10















\\"


Fig. 4.6. Isoshear lines for the pier shaded as shown above.











D D


Fig. 4.7. [sosheat lines for the pier shaded as shown above.




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